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The von Neumann/Morgenstern approach to ambiguity

Listed author(s):
  • Dumav, Martin

    (Center for Mathematical Economics, Bielefeld University)

  • Stinchcombe, Maxwell B.

    (Center for Mathematical Economics, Bielefeld University)

Registered author(s):

    A choice problem is risky (respectively ambiguous) if the decision maker is choosing between probability distributions (respectively sets of probability distributions) over utility relevant consequences. We provide an axiomatic foundation for and a representation of continuous linear preferences over sets of probabilities on consequences. The representation theory delivers: first and second order dominance for ambiguous problems; a utility interval based dominance relation that distinguishes between sources of uncertainty; a complete theory of updating convex sets of priors; a Bayesian theory of the value of ambiguous information structures; complete separations of attitudes toward risk and ambiguity; and new classes of preferences that allow decreasing relative ambiguity aversion and thereby rationalize recent challenges to many of the extant multiple prior models of ambiguity aversion. We also characterize a property of sets of priors, descriptive completeness, that resolves several open problems and allows multiple prior models to model as large a class of problems as the continuous linear preferences presented here.

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    File URL: https://pub.uni-bielefeld.de/download/2674101/2901851
    File Function: First Version, 2013
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    Paper provided by Center for Mathematical Economics, Bielefeld University in its series Center for Mathematical Economics Working Papers with number 480.

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    Length: 38
    Date of creation: 30 Apr 2014
    Handle: RePEc:bie:wpaper:480
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    2. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
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    4. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
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    10. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
    11. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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    14. Fang, Fang & Stinchcombe, Maxwell B. & Whinston, Andrew B., 2010. "Proper scoring rules with arbitrary value functions," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1200-1210, November.
    15. Massimiliano Amarante, 2015. "Analogy in Decision Making," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 1027-1041, October.
    16. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
    17. Chew, Soo Hong & Epstein, Larry G. & Zilcha, Itzhak, 1988. "A correspondence theorem between expected utility and smooth utility," Journal of Economic Theory, Elsevier, vol. 46(1), pages 186-193, October.
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    19. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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    21. Stigler, George J & Becker, Gary S, 1977. "De Gustibus Non Est Disputandum," American Economic Review, American Economic Association, vol. 67(2), pages 76-90, March.
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